Abstract. The energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitr...

For a simple connected graph G with n-vertices having Laplacian eigenvalues μ1, μ2, . . . , μn−1, μn = 0, and signless Laplacian eigenvalues q1, q2, . . . , qn, the Laplacian-energy-like invariant(LEL) and the incidence energy (IE) of a graph G are respectively defined as LEL(G) = ∑n−1 i=1 √ μi and IE(G) = ∑n i=1 √ qi. In this paper, we obtain some sharp lower and upper bounds for the Laplacian...

Averting the impending harms of climate change requires to replace fossil fuels with renewables as a primary source energy. Non-electric renewable potential being limited, this implies extending use electricity generated from wind and solar beyond power sector, either by direct electrification or synthetic fuels. Modeling transformation towards such an energy system is challenging, because it i...

The equipment information in the regional energy system is difficult to retrieve and amount of data too large realize intelligent application. In order solve problem, this paper proposes a visualization research method based on knowledge graph. Firstly, collected classified. Secondly, framework defined for unstructured data, which be recognized by computer, hidden Markov model used word segment...

Topology control in wireless sensor networks is an important issue for scalability and energy efficiency. It is often based on graph reduction performed through the use of Gabriel Graph or Relative Neighborhood Graph. This graph reduction is usually based on geometric values. In this paper we tackle the problem of possible connectivity loss in the reduced graph by applying a battery level based...

Graph cut algorithms are very popular in image segmentation approaches. However, the detailed parts of the foreground are not segmented well in graph cut minimization.There are basically two reasons of inadequate segmentations: (i) Data smoothness relationship of graph energy. (ii) Shrinking bias which is the bias towards shorter paths. This paper improves the foreground segmentation by integra...

We describe an approach to optimization based on a multiple-restart quasi-Hopfield network where the only problem-specific knowledge is embedded in the energy function that the algorithm tries to minimize. We apply this method to three different variants of the graph coloring problem: the minimum coloring problem, the spanning subgraph k-coloring problem, and the induced subgraph k-coloring pro...